On identifiability and information-regularity in parametrized normal distributions

We describe methods to establish identifiability and information-regularity of parameters in normal distributions. Parameters are considered identifiable when they are determined uniquely by the probability distribution and they are information-regular when their Fisher information matrix is full rank. In normal distributions, information-regularity implies local identifiability, but the converse is not always true. Using the theory of holomorphic mappings, we show when the converse is true, allowing information-regularity to be established without having to explicitly compute the information matrix. Some examples are given.This work was supported by the Air Force Office of Scientific Research under Grant no. F49620-93-1-0096, the National Science Foundation under Grant no. MIP-9122753, and the Office of Naval Research under Grant no. N00014-91-J-1298.     

On the concentrated stochastic likelihood function in array signal processing

The stochastic likelihood function [(STO)LF] associated with the narrowband signal processing problem can be concentrated with respect to the signal covariance matrix elements and the noise power. Although this is a known fact, no clear-cut derivation of the concentrated (STO)LF appears to be available in the literature. In this short paper we provide a simple, complete proof of the concentrated (STO)LF formula.The work of A. Nehorai was supported by the Air Force Office of Scientific Research under Grant no. F49620-93-1-0096, the Office of Naval Research under Grant no. N00014-91-J-1298, and the National Science Foundation under grant no. MIP-9122753. The work of P. Stoica was supported by the Swedish Research Council for Engineering Sciences under contract no. 93-669.     

An adaptive multiscale inverse scattering approach to photothermal depth profilometry

Photothermal depth profilometry is formulated as a nonlinear inverse scattering problem. Starting with the one-dimensional heat diffusion equation, we derive a mathematical model relating arbitrary variation in the depth-dependent thermal conductivity to observed thermal wavefields at the surface of a material sample. The form of the model is particularly convenient for incorporation into a nonlinear optimization framework for is particularly convenient for incorporation into a nonlinear optimization framework for recovering the conductivity based on thermal wave data obtained at multiple frequencies. We develop an adaptive, multiscale algorithm for solving this highly ill-posed inverse problem. The algorithm is designed to produce an accurate, low-order representation of the thermal conductivity by automatically controlling the level of detail in the reconstruction. This control is designed to reflect both (1) the nature of the underlying physics, which says that scale should decrease with depth, and (2) the particular structure of the conductivity profile, which may require a sparse collection of fine-scale components to adequately represent significant features such as a layering structure. The approach is demonstrated in a variety of synthetic examples representative of nondestructive evaluation problems seen in the steel industry.The work of authors E. L. Miller and I. Yavuz was supported by a CAREER Award from the National Science Foundation MIP-9623721, an ODDR&E MURI under Air Force Office of Scientific Research contract F49620-96-1-0028, and the Army Research Office Demining MURI under grant DAAG55-97-1-0013. The work of authors L. Nicolaides and A. Mandelis was supported by a research contract from Material and Manufacturing Ontario (MMO).     

Methods for the numerical integration of Hamiltonian systems

To compute an infinite horizon optimal controller for a linear periodic system via an invariant subspace method, the computation of the period map associated with the Hamilton-Jacobi-Bellman equations is required. In this paper we discuss methods for the numerical integration of such Hamiltonian systems. Two numerical integration techniques are introduced. A method is developed whereby symplectic invariants associated with the Hamilton-Jacobi-Bellman equations are preserved. Also, a shifting scheme is introduced that in effect swaps the roles of the stable and unstable invariant subspaces by using the semigroup property of state transition matrices. A shift is introduced into the resultant initial value problem ensuring that the eigenvalues of a differential equation reside in the region of absolute stability for an appropriate numerical integration routine. These techniques are then compared to standard numerical integration routines to ascertain their efficiency and accuracy. This research was supported by the Air Force Office of Scientific Research under Grant No. F49620-94-1-0104 DEF, and by the National Science Foundation under Grant. No. ECS-9120643.     

Nonparametric spectral analysis of gapped data via an adaptive filtering approach

We present an algorithm for nonparametric complex spectral analysis of gapped data via an adaptive finite impulse response (FIR) filtering approach, referred to as the gapped-data amplitude and phase estimation (GAPES) algorithm. The incomplete data sequence may contain gaps of various sizes. The GAPES algorithm iterates the following two steps: (1) estimating the adaptive FIR filter and the corresponding complex spectrum via amplitude and phase estimation (APES), a nonparametric adaptive FIR filtering approach, and (2) filling in the gaps via a least-squares APES fitting criterion. The initial condition for the iteration is obtained from the available data segments via APES. Numerical results are presented to demonstrate the effectiveness of the proposed GAPES algorithm.This work was supported in part by the Senior Individual Grant Program of the Swedish Foundation for Strategic Research, AFRL/SNAT, Air Force Research Laboratory, Air Force Material Command, USAF, under grant number F33615-99-1-1507, and the National Science Foundation Grant MIP-9457388. The US Government is authorized to reproduce and distribute reprints for Governmental purposes notwithstanding any copyright notice thereon.     

Passivation of GaAs surfaces*

Exposure to atomic hydrogen lowers the decomposition temperature of GaAs. Simultaneous exposure of GaAs to atomic hydrogen and atomic nitrogen above 500°C results in a layer rich in GaN. The degree of passivation was monitored by photoluminescence. A fourfold improvement in luminescence efficiency was obtained by nitridization, while a factor-of-ten improvement can be obtained with the more complicated technique of generating an (AlGa)As skin. This research was supported by the Air Force Office of Scientific Research under Contract No. F49620-80-C-0039.     

Index two linear time varying singular systems of differential equations

Linear time varying singular systems of differential equations of the formA(t)x(t) + B(t)x(t)=f(t) whereA(t) is singular and the system has index at most two are considered. Recent results on their analytic solution are improved on. Examples are given that show these results are not easily extended.This work was supported in part by the National Science Foundation under Grant No. DMS-8318026 and the Air Force Office of Scientific Research under Grant No. 84-0240.     

Using tabu search to solve the Steiner tree-star problem in telecommunications network design

We present a study of using tabu search to solve a specific network design problem arising in the telecommunication industry. We develop a tabu search heuristic for this problem that incorporates long-term memory and probabilistic move selections. Computational results show that the new heuristic consistently outperforms the best local search currently available, with significantly increased performance differences on more difficult problems.This research was supported in part by Air Force Office of Scientific Research AASERT Grant No. F49620-92-J-0248-DEF.     

A column generation algorithm for bandwidth packing

We describe a column generation branch and bound procedure for optimally solving the bandwidth packing problem. The objective of this problem is to allocate bandwidth in a telecommunications network to maximize total revenue. The problem is formulated as an integer programming problem and the linear programming relaxation solved using column generation and the simplex algorithm. A branch and bound procedure which branches upon a particular path being used for a bandwidth routing is used to solve the IP. We present computational results.This research was partially supported by a grant from the Colorado Advanced Software Institute and by Air Force Office of Scientific Research and Office of Naval Research Contract Nos. F49620-90-C-0033 and F49620-92-J-0248-DEF.     

Comparative performance study of element-space and beam-space MUSIC estimators

The goal of this paper is to show that in large samples the variances of the direction-of-arrival (DOA) estimates provided by the element-space MUSIC (i.e., MUSIC applied directly to the sensor output data) are always less than the corresponding variances associated with the beam-space MUSIC (i.e., MUSIC applied to spatially filtered sensor data).The work of A. Nehorai was supported by a grant from the Air Force Office of Scientific Research, under Grant No. AFOSR-90-0164 and the Office of Naval Research under Grant No. N00014-91-J-1298.     

The running time-frequency distributions

This paper introduces the running kernels that yield recursive structures for time-frequency distributions (TFDs). The running kernels offer important properties not possessed by the commonly used block distribution kernels. The introduced kernels allow an invariance in computations with respect to the extent of the kernel in the time or the lag variable. However, contrary to the wide class of block kernels that satisfy the desired timefrequency (t-f) properties, most recursive (running) time-frequency distributions (RTFDs) violate the marginal and the support properties. This paper considers both the direct and the indirect types of recursion and presents examples for illustration.This research was supported in part by the US Air Force, grant no. AFOSR F49620-93-C0063 and a grant from the Office of Research and Sponsored Projects at Villanova University.     

Dispersion control in magnetostatic wave delay lines

A major impediment to the realization of practical magnetostatic wave (MSW) devices is the inherent non-linear delay versus frequency characteristics of MSW delay lines. Most device applications require either nondispersive (delay vs. frequency slope=0) or linearly dispersive (delay vs. frequency slope = constant) characteristics. There are four basic approaches to the elimination and/or linearization of MSW dispersion: (1) modification of the magnetic film properties as a function of film thickness, (2) modification of the ground plane geometry, (3) modification of the bias field uniformity, and (4) perturbation of the propagation path surface with metal electrode reflective arrays. In principle all four approaches can yield either linearly dispersive or nondispersive characteristics with a suitable choice of bias field orientation and critical design parameters. These dispersion control techniques are reviewed, and data from recent experiments demonstrating the strengths and weaknesses of the various approaches are discussed. To date the most extensive experimental work has been done with the multiple layer (magnetic properties varied as a function of film thickness) and ground-plane spacing techniques. At present the ground-plane spacing technique produces results acceptable for some systems applications, while the multiple-layer approach is still under development.Research supported in part by Air Force Office of Scientific Research (AFSC), United States Air Force, under contract Number F49620-82-C-0081 and Rome Air Development Center (RADC), United States Air Force, under Contract Number F19628-82-C-0098. The United States Government is authorized to-reproduce and distribute reprints for governmental purposes notwithstanding any copyright notation herein.     

Direction-of-arrival estimation in applications with multipath and few snapshots

This paper analyzes two direction-of-arrival (DOA) estimation algorithms used in the presence of multipath propagation and with very few snapshots. The conditional maximum likelihood (CML) algorithm and the method of direction estimation (MODE) are discussed. The estimates provided by these algorithms are shown to coincide for large number of snapshots or large signal-to-noise ratio. Necessary and sufficient conditions are derived for the algorithms to yield unique estimates. It is shown that their uniqueness conditions coincide with the minimal uniqueness condition on the array, that is independent of the algorithm used (if the array does not satisfy this minimal condition, no DOA estimation method can give unique estimates). Numerical examples are presented to demonstrate the theoretical results.The work of A. Nehorai and D. Starer was supported by the Air Force Office of Scientific Research under Grant No. AFOSR-90-0164 and by the Office of Naval Research under Grant No. N00014-91-J-1298.     

One canonical form for higher-index linear time-varying singular systems

One form of the singular systemAx+Bx=f is considered. The analytic solution, perturbation, and numerical solution of this form are examined. A class of systems which may be transformed into this form without altering these properties is characterized.Research sponsored by Air Force Office of Scientific Research, Air Force Systems Command, under Grant No. AFOSR-81-0052A. The United States Government is authorized to reproduce and distribute reprints for governmental purposes not with-standing any copyright notation here on.     

Design and fabrication of sub-μs silicon-on-insulator thermo-optic 4×4 switch matrix

A rearrangeable nonblocking silicon-on-insulator-based thermo-optic 4x4 switch matrix with spot size converters （SSCs） and a new driving circuit are designed and fabricated. The introduction of a spot size converter （SSC） has decreased the insertion loss to less than 10dB and the new driving circuit has improved the response speed to less than l~s.     

Asymptotically robust detection in partially contaminated noise

We consider the discrete-time detection of a known time-varying deterministic signal in white noise, where the univariate noise density is known perfectly only on an interval about the origin. We present a method to enhance the asymptotic performance of the detector by exploiting this knowledge, and at the same time preserve robustness properties of the detector to the remaining inexact knowledge of the univariate noise density. We then provide examples to show that improved performance is indeed obtained.This research was supported by the Air Force Office of Scientific Research under Grant AFOSR-82-0033.     

Optimal Hankel-norm approximation of continuous-time linear systems

A problem on optimal approximation of continuous-time linear systems is studied. The performance measure (error) is chosen to be the spectral norm of the difference between the Hankel operators associated with the original system and the approximant. It is shown that the Hankel operators associated with continuous-time systems and the Hankel matrices associated with discrete-time systems are related by an interesting correspondence property via bilinear transforms. This fact is then used to derive the continuous-time results (theory and algorithms) from the established discrete-time ones. Some simple examples are presented.This research was supported by the Army Research Office under Grant No. DAAG 29-79-C-0054, and by the National Science Foundation Grant No. ENG-7908673, and by the Office of Naval Research under Contract No. N000-14-81-K-0191.Formerly with the Department of Electrical Engineering-Systems, University of Southern California, Los Angeles, California 90007, USA     

A quasi-parametric algorithm for synthetic aperture radar target feature extraction and imaging with angle diversity

We present synthetic aperture radar (SAR) target feature extraction and imaging techniques with angle divesity. We first establish a flexible data model that describes each target scatterer as a two-dimensional (2D) complex sequence with arbitrary amplitude and constant phase in range and cross-range. A new algorithm, referred to as the QUasiparametric ALgorithm for target feature Extraction (QUALE), is then presented for SAR target feature extraction via data fusion through angle diversity based on the flexible data model. QUALE first estimates the model parameters, which include, for each scatterer, a 2D arbitrary real-valued amplitude sequence, a constant phase, and scatterer locations in range and cross-reange. QUALE then averages the estimated 2D real-valued amplitude sequence over range by making the assumption that the scatterer radar cross section is approximately consant. QUALE next models the so-obtained 1D sequence with a simple sinc function by assuming that the scatterer is approximately a dihedral (a trihedral is approximated as a very short dihedral) and estimates the relevant sinc function parameters by minimizing a nonlinear least-squares fitting function. Finally, the approximate 2D SAR image is reconstructed by using the estimated features. Numerical examples are given to demonstrate the perfomance of the proposed algorithm.This work was supported in part by AFRL/SNAT, Air Force Research Laboratory, Air Force Materiel Command, USAF, under grant no. F33615-99-1-1507, and the National Science Foundation Grant MIP-9457388. The U.S. Goverment is authorized to reproduce and distribute reprints for Governmental purposes notwithstanding any copyright notation thereon.     

Convergence analysis of an adaptive pseudolinear-regression notch filtering algorithm

This paper analyzes the convergence properties of an adaptive pseudolinear regression notch filtering algorithm recently proposed in the literature for estimating the frequencies of multiple sine waves from measurements corrupted by possibly colored additive noise. Simple necessary and sufficient conditions for the local convergence of this algorithm to the true frequency values are derived. It is shown that the algorithm has an interesting decoupling property in the sense that satisfaction of the convergence condition by a certain frequency implies local convergence to that frequency no matter whether the other frequencies satisfy or do not satisfy the convergence conditions. However, it is also shown that the algorithm is not generally convergent and, therefore, cannot be recommended for widespread use in applications. Numerical examples are used to illustrate the main points in the theoretical analysis.The work of A. Nehorai was supported by the Air Force Office of Scientific Research, under Grant No. AFOSR-90-0164.     

Capon estimation of covariance sequences

Estimating the covariance sequence of a wide-sense stationary process is of fundamental importance in digital signal processing (DSP). A new method, which makes use of Fourier inversion of the Capon spectral estimates and is referred to as theCapon method, is presented in this paper. It is shown that the Capon power spectral density (PSD) estimator yields an equivalent autoregressive (AR) or autoregressive moving-average (ARMA) process; hence, theexact covariance sequence corresponsing to the Capon spectrum can be computed in a rather convenient way. Also, without much accuracy loss, the computation can be significantly reduced via an approximate Capon method that utilizes the fast Fourier transform (FFT). Using a variety of ARMA signals, we show that Capon covariance estimates are generally better than standard sample covariance estimates and can be used to improve performances in DSP applications that are critically dependent on the accuracy of the covariance sequence estimates.This work was supported in part by National Science Foundation Grant MIP-9308302, Advanced Research Project Agency Grant MDA-972-93-1-0015, the Senior Individual Grant Program of the Swedish Foundation for Strategic Research and the Swedish Research Council for Engineering Sciences (TFR).